So as written this question specifically asks about a Bitcoin-centric rollup on Ethereum. This means we can avoid a discussion of rollups on Bitcoin specifically. But I’ll dwell on this briefly. I have been an advocate of distinguishing the Bitcoin asset and the network (i.e., tokenizing Bitcoin and allowing it to settle on a variety of transactional media – whether that’s LN bitcoin, Bitcoin-native rollups, other blockchains, or other databases (like the Coinbase database)). I would analogize this to the USD network. Dollars don’t just settle as cash, or as push payments in the Fedwire system, but in all kinds of different settings – ACH, debit, credit, Fednow, wires, correspondent banks, money orders, checks, interbank settlement networks, gift cards, internal databases like Paypal, Venmo, Zelle, etc. Similarly, I want to see Bitcoin liberated as a Medium of Exchange from the tyranny of its own transactional network. This doesn’t mean reducing the number of mainchain settlements, but simply vastly broadening the utility of Bitcoin by making it usable in many other domains, thus ultimately driving up fees on the base layer itself (as these non-Bitcoin-network transactions would have to eventually settle to Bitcoin). The objective is to increase the economic and semantic density as much as possible and I believe making Bitcoin as a collateral useful in many other domains ultimately increases the security of the network on net, without overly adding to reorg risk. (One quick sidenote: as Vitalik I believe has mentioned, Proof of Reserve ideas ultimately intersect with rollups, and since Bitcoiners are generally pro PoR (at least the smart ones are, that realize we will inevitably have custodial intermediation somewhere), you could imagine that they would eventually see the value for a ZK rollup.)
 
If I were marketing a new rollup to Bitcoiners I would first and foremost aim to build it on the Bitcoin L1 specifically. Most Bitcoiners do not share my perspective around tokenizing BTC and using it on a variety of transactional domains, but I believe that many Bitcoiners are open to the idea of Bitcoin native L2s (even non-LN ones). A Bitcoin native rollup would require a new ZKP verifier to Bitcoin Core as we know. This would mean a soft fork. There are firms working on this and I am optimistic about this pathway. A sovereign rollup should be doable on Bitcoin too as well using the blobspace made available via inscriptions, and wouldn’t require a soft fork. But a sovereign rollup is ultimately not long term satisfactory, since there is no trustless bridge between mainchain assets and the rollups. But a sovereign rollup is appealing because it could migrate to a new L1, so you can always start one on Ethereum (if you’re so inclined) and move it to Bitcoin as a full validity rollup if a soft fork comes through.
 
But this wasn’t the question! The question is about a Bitcoin rollup on Ethereum. This is a good approach, since many rollups exist on Ethereum and we’re not starting from scratch. I believe ZK rollups are more appetizing to Bitcoiners than optimistic rollups, given Bitcoiners’ historical aversion to fraud proofs (granted, LN uses fraud proofs but this fact isn’t commonly acknowledged) and general desire for technically complete, even if difficult solutions (as opposed to worse-is-better cludgy solution). So I would go with a ZK rollup. Since we’re marketing to Bitcoiners, I would want three conditions to obtain:
 

• The collateral in the rollup has to relate to BTC itself – i.e. as liquidity is deposited in the rollup it has to ultimately be accretive to the value of Bitcoin
• The rollup has to be as trust minimized as possible
• The rollup has to have a value prop that aligns with Bitcoin values
• (Optional): the rollup has to avoid using ETH specifically

 
On the first point, this means that we have to tokenize Bitcoin somehow and port it over to Ethereum. Here we immediately run into a conflict with point 2, since there aren’t many trustless tokenized Bitcoin systems. tBTC is one option but it is small for now. I find it complex, and capital inefficient. One interesting way to go if we’re not too concerned about capital inefficiency would be a Bitcoin-backed stablecoin. There’s two ways to do this semi trustlessly and still have value accrete back to Bitcoin: a system like the original DAI (except backed just by Bitcoin rather than just by ETH), which I think Reflexer labs has suggested they want to work on. Alternatively, a synthetic Bitcoin stablecoin, which several folks are working on. You would achieve this exposure by combining a spot long with a short position (the basis trade) and in theory you are generally getting paid to keep the position on. I think the DAI approach is best. Bitcoiners are generally supportive of stablecoins so I don’t see this as too hostile to the Bitcoin philosophy.
 
Regarding Bitcoin values, the rollup on its own scales Bitcoin without making unacceptable trust tradeoffs so I think that aligns with Bitcoin values. If you can create private p2p cash-type transactions with Bitcoin collateral in a way that ultimately augments fees on the Bitcoin mainchain, that will satisfy all but the most hardcore Bitcoiners. (Stablecoin-skeptic and tokenized-bitcoin-skeptic Bitcoiners will fall in line within the next 12 months in my opinion, when the sheer force of market evidence becomes undeniable. There isn’t a big discussion of rollups in the Bitcoin community right now but I do expect that moderates will be on board soon enough).  
 
Regarding the optional fourth point, no current rollup on Ethereum as far as I know supports gas payments in wrapped bitcoin, so we would have to envision a new, theoretical rollup. Technically I don’t see any dealbreakers here. As far as I understand it’s possible to pay for L1 fees in non-ETH, so I think the entire rollup could use wrapped Bitcoin as an ERC20 even if it’s settling to Ethereum. (I think there must be a catch here because I see fee abstraction as hostile to ETH’s value prop but if there is I am missing it).
 
In terms of L2 stacks, I would favor the Starknet stack, since it is Cairo based and thus inherently designed to be ZK proven. This seems more in line with the Bitcoin design philosophy – doing it right with a purpose-built programming language, rather than inheriting the technical debt and zk-hostility of EVM/Solidity. Alternatively, in terms of achieving a positioning that is likely to be favorably received by Bitcoiners who value privacy, you could model it off a privacy-focused rollup like Aztec network. I don’t believe Aztec could work off the shelf with tokenized Bitcoin collateral though.
 
In terms of market positioning, I would market this to moderate Bitcoiners (the hardliners will reject anything built on Ethereum at all) and pro-Bitcoin crypto users generally. I would try to identify who is actively transacting with Bitcoin and is looking for cost savings or efficiency gains that come with a rollup. So I would look at people that use wBTC and may be looking for a less trusted product but are nevertheless comfortable with the Ethereum ecosystem. Exchanges, market makers, prop funds aiming to settle Bitcoin with each other with faster settlement could also be worthwhile anchor tenants. But overall I think it’s hard to forecast who will get the most benefit out of this because the use cases tend to emerge once the transactional space is created, and it’s hard to predict who would derive the most value out of a fast settling, private form of Bitcoin.